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Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam
date Tue, 19 Nov 2019 14:52:55 +0000
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Chris@82 3 <!-- This manual is for FFTW
Chris@82 4 (version 3.3.8, 24 May 2018).
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Chris@82 6 Copyright (C) 2003 Matteo Frigo.
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Chris@82 24 <head>
Chris@82 25 <title>FFTW 3.3.8: Advanced Complex DFTs</title>
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Chris@82 36 <link href="Advanced-Interface.html#Advanced-Interface" rel="up" title="Advanced Interface">
Chris@82 37 <link href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" rel="next" title="Advanced Real-data DFTs">
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Chris@82 68 </head>
Chris@82 69
Chris@82 70 <body lang="en">
Chris@82 71 <a name="Advanced-Complex-DFTs"></a>
Chris@82 72 <div class="header">
Chris@82 73 <p>
Chris@82 74 Next: <a href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" accesskey="n" rel="next">Advanced Real-data DFTs</a>, Previous: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="p" rel="prev">Advanced Interface</a>, Up: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="u" rel="up">Advanced Interface</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
Chris@82 75 </div>
Chris@82 76 <hr>
Chris@82 77 <a name="Advanced-Complex-DFTs-1"></a>
Chris@82 78 <h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>
Chris@82 79
Chris@82 80 <div class="example">
Chris@82 81 <pre class="example">fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
Chris@82 82 fftw_complex *in, const int *inembed,
Chris@82 83 int istride, int idist,
Chris@82 84 fftw_complex *out, const int *onembed,
Chris@82 85 int ostride, int odist,
Chris@82 86 int sign, unsigned flags);
Chris@82 87 </pre></div>
Chris@82 88 <a name="index-fftw_005fplan_005fmany_005fdft"></a>
Chris@82 89
Chris@82 90 <p>This routine plans multiple multidimensional complex DFTs, and it
Chris@82 91 extends the <code>fftw_plan_dft</code> routine (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) to
Chris@82 92 compute <code>howmany</code> transforms, each having rank <code>rank</code> and size
Chris@82 93 <code>n</code>. In addition, the transform data need not be contiguous, but
Chris@82 94 it may be laid out in memory with an arbitrary stride. To account for
Chris@82 95 these possibilities, <code>fftw_plan_many_dft</code> adds the new parameters
Chris@82 96 <code>howmany</code>, {<code>i</code>,<code>o</code>}<code>nembed</code>,
Chris@82 97 {<code>i</code>,<code>o</code>}<code>stride</code>, and
Chris@82 98 {<code>i</code>,<code>o</code>}<code>dist</code>. The FFTW basic interface
Chris@82 99 (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) provides routines specialized for ranks 1, 2,
Chris@82 100 and&nbsp;3, but the advanced interface handles only the general-rank
Chris@82 101 case.
Chris@82 102 </p>
Chris@82 103 <p><code>howmany</code> is the (nonnegative) number of transforms to compute. The resulting
Chris@82 104 plan computes <code>howmany</code> transforms, where the input of the
Chris@82 105 <code>k</code>-th transform is at location <code>in+k*idist</code> (in C pointer
Chris@82 106 arithmetic), and its output is at location <code>out+k*odist</code>. Plans
Chris@82 107 obtained in this way can often be faster than calling FFTW multiple
Chris@82 108 times for the individual transforms. The basic <code>fftw_plan_dft</code>
Chris@82 109 interface corresponds to <code>howmany=1</code> (in which case the <code>dist</code>
Chris@82 110 parameters are ignored).
Chris@82 111 <a name="index-howmany-parameter"></a>
Chris@82 112 <a name="index-dist"></a>
Chris@82 113 </p>
Chris@82 114
Chris@82 115 <p>Each of the <code>howmany</code> transforms has rank <code>rank</code> and size
Chris@82 116 <code>n</code>, as in the basic interface. In addition, the advanced
Chris@82 117 interface allows the input and output arrays of each transform to be
Chris@82 118 row-major subarrays of larger rank-<code>rank</code> arrays, described by
Chris@82 119 <code>inembed</code> and <code>onembed</code> parameters, respectively.
Chris@82 120 {<code>i</code>,<code>o</code>}<code>nembed</code> must be arrays of length <code>rank</code>,
Chris@82 121 and <code>n</code> should be elementwise less than or equal to
Chris@82 122 {<code>i</code>,<code>o</code>}<code>nembed</code>. Passing <code>NULL</code> for an
Chris@82 123 <code>nembed</code> parameter is equivalent to passing <code>n</code> (i.e. same
Chris@82 124 physical and logical dimensions, as in the basic interface.)
Chris@82 125 </p>
Chris@82 126 <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
Chris@82 127 the input or output arrays is located at <code>j*istride</code> or
Chris@82 128 <code>j*ostride</code>, respectively. (For a multi-dimensional array,
Chris@82 129 <code>j</code> is the ordinary row-major index.) When combined with the
Chris@82 130 <code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
Chris@82 131 that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
Chris@82 132 (The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
Chris@82 133 <a name="index-stride-1"></a>
Chris@82 134 </p>
Chris@82 135
Chris@82 136 <p>For in-place transforms, the input and output <code>stride</code> and
Chris@82 137 <code>dist</code> parameters should be the same; otherwise, the planner may
Chris@82 138 return <code>NULL</code>.
Chris@82 139 </p>
Chris@82 140 <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
Chris@82 141 this function returns. You can safely free or reuse them.
Chris@82 142 </p>
Chris@82 143 <p><strong>Examples</strong>:
Chris@82 144 One transform of one 5 by 6 array contiguous in memory:
Chris@82 145 </p><div class="example">
Chris@82 146 <pre class="example"> int rank = 2;
Chris@82 147 int n[] = {5, 6};
Chris@82 148 int howmany = 1;
Chris@82 149 int idist = odist = 0; /* unused because howmany = 1 */
Chris@82 150 int istride = ostride = 1; /* array is contiguous in memory */
Chris@82 151 int *inembed = n, *onembed = n;
Chris@82 152 </pre></div>
Chris@82 153
Chris@82 154 <p>Transform of three 5 by 6 arrays, each contiguous in memory,
Chris@82 155 stored in memory one after another:
Chris@82 156 </p><div class="example">
Chris@82 157 <pre class="example"> int rank = 2;
Chris@82 158 int n[] = {5, 6};
Chris@82 159 int howmany = 3;
Chris@82 160 int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
Chris@82 161 between the first element
Chris@82 162 of the first array and the
Chris@82 163 first element of the second array */
Chris@82 164 int istride = ostride = 1; /* array is contiguous in memory */
Chris@82 165 int *inembed = n, *onembed = n;
Chris@82 166 </pre></div>
Chris@82 167
Chris@82 168 <p>Transform each column of a 2d array with 10 rows and 3 columns:
Chris@82 169 </p><div class="example">
Chris@82 170 <pre class="example"> int rank = 1; /* not 2: we are computing 1d transforms */
Chris@82 171 int n[] = {10}; /* 1d transforms of length 10 */
Chris@82 172 int howmany = 3;
Chris@82 173 int idist = odist = 1;
Chris@82 174 int istride = ostride = 3; /* distance between two elements in
Chris@82 175 the same column */
Chris@82 176 int *inembed = n, *onembed = n;
Chris@82 177 </pre></div>
Chris@82 178
Chris@82 179 <hr>
Chris@82 180 <div class="header">
Chris@82 181 <p>
Chris@82 182 Next: <a href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" accesskey="n" rel="next">Advanced Real-data DFTs</a>, Previous: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="p" rel="prev">Advanced Interface</a>, Up: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="u" rel="up">Advanced Interface</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
Chris@82 183 </div>
Chris@82 184
Chris@82 185
Chris@82 186
Chris@82 187 </body>
Chris@82 188 </html>